Abstract
The CNOT gate is a two-qubit gate which is essential for universal quantum computation. A well-established approach to implement it within Majorana-based qubits relies on subsequent measurement of (joint) Majorana parities. We propose an alternative scheme which operates a protected CNOT gate via the holonomic control of a handful of system parameters, without requiring any measurement. We show how the adiabatic tuning of pair-wise couplings between Majoranas can robustly lead to the full entanglement of two qubits, insensitive with respect to small variations in the control of the parameters.
Highlights
Topological quantum computation (TQC) is an approach to quantum computing that aims at minimizing decoherence at the hardware level, by exploiting topological properties of nonlocal degrees of freedom composed of non-Abelian anyons [1,2,3]
The braiding of a single pair of Majorana zero-energy modes (MZMs) can be realized in several ways, which are all equivalent to a physical exchange of the two non-Abelian anyons [24,25,26,27,28,29,30]
By considering the presence of additional ancilla Majoranas, we can perform braiding by properly tuning pair-wise couplings between different MZMs [31, 32], or by performing sequential projective parity measurements [8, 33,34,35,36,37,38]
Summary
Topological quantum computation (TQC) is an approach to quantum computing that aims at minimizing decoherence at the hardware level, by exploiting topological properties of nonlocal degrees of freedom composed of non-Abelian anyons [1,2,3]. The key idea of holonomic quantum computation is to exploit non-Abelian geometrical phases to implement unitary operations on a degenerate eigenspace of the underlying Hamiltonian [47]. Those gauge-invariant phases emerge when the parameters of the system are tuned along degeneracy-preserving closed loops in parameter space. The braiding of Majoranas itself can be interpreted as a holonomic process, where the system follows specific, topologically-protected loops in the three-dimensional parameter space of pair-wise Majorana couplings [8, 31]. It is possible to tune the coupling strengths cj away from the idle configuration without destroying the qubit, keeping the fixed-parity computational space degenerate and separated from the excited states by a finite energy gap. A sufficient condition for the stability of the qubit is that, at each time t, either one or two of the five different couplings strengths cj must be non-vanishing [31,50,51]
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